Question

Show your work, please

1. Counting and Pigeonhole Principle (a). A set of four different integers is chosen at random between 1 and 200 (inclusive). How many different outcomes are possible? (b). How many different integers between 1 and 200 (inclusive) must be chosen to be sure that at least 3 of them are even? (C). How many different integers between 1 and 200 (inclusive) mu be chosen to be sure that at least 2 of them add up to 20? (d). How many different integers between 1 and 200 (inclusive) must be chosen to be sure that at least one of them contains the digit 5? (For example, {11, 35, 42} has an integer that contains the digit 5, while {2,48, 71,96} does not.)

Answer 1

one 3t @ The set of inlegen betren a cand 200 which are Contach 5 S 5,15, 25, 195, 195, $9, 150, 157 - - راکر50 159,}; odreash - Brugere mi sz) - 20+10+10-/-/ = 38 os The number of different Integer betwen 1 and 200 (include) must be chosen to be sure that at 380 x 1626 5 38) 6 x 16220 + 386 1 x 162 162 + 37038030 11 38 (4 Х 1626
2
@ The set of Intiger in $={1,2,3, 200} A set of four defferent infegers in chonen. at random betwen 1 and 200 Inclusive the number of outcomes are 200 C4 2.) number even integer be 100 S; = {2,4,6;... 200} Namber of de chosen to sure that at least 3 of 4 integer (chosen from 1 to 200 are even 200 6 4 684 9.50 b set i in 100 ci х 100 g 100 Co + x 100 to Cry 3 3 even 1 Odd no odd 4 even 20091225 The odd number up to 20 is io Set Sq 2 {1, 2, 51.19} The number of different inleges beteren and wo (include, must be chosen to be sure that at least 2 of them and up 10 Cox 19°C2 + loc + 100 x 180C, +10 C4 x 190 € 2 of seff 1 to 20 in Х others 3 odd of others goodd and on S₂ Ophen 830985
1